SATHEE: Quantitative Aptitude Ques 108

Quantitative Aptitude Ques 108

Question: If $ \theta $ is an acute angle and $ {{\tan }^{2}}\theta +\frac{1}{{{\tan }^{2}}\theta }=2, $ then the value of $ \theta $ is

Options:

A) $ 45{}^\circ $

B) $ 30{}^\circ $

C) $ 60{}^\circ $

D) $ 15{}^\circ $

Show Answer

Answer:

Correct Answer: A

Solution:

Given, $ {{\tan }^{2}}\theta +\frac{1}{{{\tan }^{2}}\theta }=2 $
$ \Rightarrow $ $ \frac{{{\tan }^{4}}\theta +1}{{{\tan }^{2}}\theta }=2 $

$ \Rightarrow $ $ {{\tan }^{2}}\theta -2{{\tan }^{2}}\theta +1=\theta $ Let $ y={{\tan }^{2}}\theta $

$ \therefore $ $ y^{2}-2y+1=0 $

$ \Rightarrow $ $ y^{2}-y-y+1=0 $

$ \Rightarrow $ $ y,(y-1)-1,(y-1)=0 $

$ \Rightarrow $ $ (y-1)(y-1)=0 $

$ \therefore $ $ y=1 $ $ \because $ $ tan^{2}\theta =1 $

$ \Rightarrow $ $ \tan \theta =\pm ,1 $
$ \Rightarrow $ $ \theta =45{}^\circ , $ $ 135{}^\circ $ But $ \theta $ is an acute angle, therefore $ \theta =45{}^\circ $

Quantitative Aptitude Ques 107

Quantitative Aptitude Ques 109

Quantitative Aptitude Ques 108

Question: If $ \theta $ is an acute angle and $ {{\tan }^{2}}\theta +\frac{1}{{{\tan }^{2}}\theta }=2, $ then the value of $ \theta $ is

Options:

Answer:

Solution:

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